Simplify the following expression: $k = \dfrac{-9p^2 + 45p - 36}{p - 4} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-9$ , so we can rewrite the expression: $ k =\dfrac{-9(p^2 - 5p + 4)}{p - 4} $ Then we factor the remaining polynomial: $p^2 {-5}p + {4} $ ${-4} {-1} = {-5}$ ${-4} \times {-1} = {4}$ $ (p {-4}) (p {-1}) $ This gives us a factored expression: $\dfrac{-9(p {-4}) (p {-1})}{p - 4}$ We can divide the numerator and denominator by $(p + 4)$ on condition that $p \neq 4$ Therefore $k = -9(p - 1); p \neq 4$